What is the integral of 1/(x*ln(2x)) ?

The integral of 1/(x*ln(2x)) is ln|ln(2x)|+C

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integral of 1/(x*ln(2x))

\int \frac{1}{x \cdot ln ( 2 x )} d x

ln ∣ ln (2 x) ∣ + C

Solution steps

\int \frac{1}{x ln ( 2 x )} d x

Apply u-substitution

: \int \frac{1}{u ln ( u )} d u

= \int \frac{1}{u ln ( u )} d u

Apply u-substitution

: \int \frac{1}{v} d v

= \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln ∣ ln (2 x) ∣

Add a constant to the solution

= ln ∣ ln (2 x) ∣ + C

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What is the integral of 1/(x*ln(2x)) ?
The integral of 1/(x*ln(2x)) is ln|ln(2x)|+C